(Bloomberg) -- Home from the Group of 20 meeting in Germany, President Donald Trump tweeted that he’d discussed creating a cyber security unit with Russian President Vladimir Putin -- drawing howls of criticism from fellow Republicans as well as Democrats.

“It’s not the dumbest idea I’ve ever heard, but it’s pretty close.” Republican Senator Lindsey Graham of South Carolina said on NBC’s “Meet the Press” in response.

At the same time Trump was signaling a desire to move beyond Russian hacking in the 2016 presidential election, Secretary of State Rex Tillerson said at a briefing in Kiev that sanctions on Russia will remain in place until Moscow meets its commitments on Ukraine under the Minsk agreement.

Trump’s tweets followed a New York Times story late Saturday that the president’s son, son-in-law and then-campaign manager met in 2016 with a Russian lawyer who has connections to the Kremlin -- the latest sign of contacts between top levels of the Republican’s team and Russia that’s the focus of numerous investigations. On Sunday, the newspaper reported that the lawyer had promised compromising information on Democratic presidential candidate Hillary Clinton.

After suggesting working with Russia on an “impenetrable” cybersecurity unit, Trump said that sanctions on Russia weren’t discussed during his meeting with Putin during the summit. “Nothing will be done until the Ukrainian & Syrian problems are solved!’’ he told his 33.5 million Twitter followers.

The statements sent conflicting signals as Trump continues to seek better U.S. relations with Russia that have been stymied as the president’s critics question his support for Putin and investigations continue into his campaign’s contacts with Russia.

Putin’s Denial

Trump, who didn’t give closing remarks or hold a press conference at the G-20 meeting, said on Twitter that he’d raised election meddling with Putin twice, and that the Russian president “vehemently denied it. I’ve already given my opinion.” Trump has said while he thinks Russia was involved in the hacking, other countries also could be to blame.

Trump doesn’t believe Putin’s denial, Chief of Staff Reince Priebus said on “Fox News Sunday,” while Treasury Secretary Steven Mnuchin, who was part of the president’s entourage in Hamburg, said on ABC’s “This Week” that it “makes no sense” to provide the content of the Trump-Putin meeting.

The president’s critics mocked Trump’s comment on Putin having “vehemently denied” Russian meddling, and questioned the president’s demeanor in his first face-to-face meeting with his counterpart.

“When pursuing a corrupt politician, mobster or murderer on strong FBI evidence, if he ‘vehemently denied it,’ we just dropped it usually,” former U.S. Attorney Preet Bharara tweeted.

Former CIA Director John Brennan said he doubted whether Trump pressed Putin hard on the election hacking.

‘Dishonorable Thing’

“I seriously question whether or not Mr. Putin heard from Mr. Trump what he needed to about the assault on our democratic institutions of the election,” Brennan said on NBC’s “Meet the Press.” “He said it’s an honor to meet President Putin. An honor to meet the individual who carried out the assault against our election? To me, it was a dishonorable thing to say.”

Russia’s interference in the 2016 U.S. election is an obstacle to improved ties between the two countries and must be dealt with to assure Americans that it doesn’t happen again, Tillerson said on a visit to Ukraine on Sunday.

Tillerson, who attended the meeting with Trump and Putin along with his Russian counterpart Sergei Lavrov and translators, was asked to confirm whether Russia’s account of the meeting was true: that Trump accepted Putin’s denial that Russia interfered in the elections.

“In all candidness, we did not expect an answer other than the one we received,” Tillerson said. “The point was made that this was an issue that really has the American people quite concerned and again it too stands as an obstacle to our ability to improve our relationship between the United States and Russia and it needs to be addressed.”

Critics Pounce

The remarks struck a slightly more confrontational tone than those Tillerson made to reporters in Hamburg after the meeting, when he said re-litigating the past would not be helpful and it was time for the U.S. and Russia to move on.

Trump cited the cease-fire in parts of Syria announced after his meeting with Putin as evidence of success, but his comment about “forming an impenetrable Cyber Security unit’’ with Russia to guard against future election interference raised eyebrows.

“Partnering with Putin on a ‘Cyber Security Unit’ is akin to partnering with Assad on a ‘Chemical Weapons Unit,’ ” Republican Senator Marco Rubio of Florida said on Twitter. Former Defense Secretary Ash Carter said on CNN’s “State of the Union” that suggesting such a unit with Russia “is like the guy who robbed your house proposing a working group on burglary.”

Graham said Trump has a “blind spot” when it comes to Putin, and that Trump is only empowering the Russian president and hurting himself. “This whole idea about moving forward without punishing Russia is undercutting his entire presidency,” Graham said.

‘Dangerously Naive’

Representative Adam Schiff of California, the top Democrat on the House Intelligence Committee, said Russia can’t be a credible partner in any cybersecurity unit. “That would be dangerously naïve,” Schiff said on CNN’s “State of the Union.” “If that’s our best election defense, we might as well just mail our ballot boxes to Moscow.”

Meanwhile, representatives of Donald Trump Jr. and Jared Kushner confirmed that 2016 Trump Tower meeting with Russian lawyer Natalia Veselnitskaya, reported by the New York Times, had taken place as reported.

Priebus dismissed the meeting as “a nothingburger” that he said was about Russia’s policy on foreign adoptions. “It was a nothing meeting,” he said. Asked why such high-level Trump officials would have a meeting about Russian adoption policy, Priebus said, “you’re going to have to talk to them.”

Mark Corallo, a spokesman for Trump’s legal team, said in a statement Sunday that “the president was not aware of and did not attend the meeting.”